When dividing `x^2+ ax + b` by (x -2) and (x-3) the remainder is zero. What are the numbers a and b.

p(x) = (4x^2 - 1)(x + 2) . Write p(x) as the product of first degree factors. Write p(x) in the form of a third degree polynomial. What is the remainder obtained by dividing 4x^3 + 6x^2- x + 2 by (x + 2). What is the remainder obtained by dividing 4x^3+6x^2-x+1 by (2x-1).

When x^3 - 2x^2+ kx + 7 is divided by ( x- 4) remainder is 11.Find k.

When (x-1) (x-2) (x-3)+ 2x+k is divided by (x-1),the remainder is 10. Then find out the remainder when it is divided by (x-2).

The quotient is x^2-5x+6 when the polynomial p(x) is divided by (x-1), and the remainder is 7.Then:- Find P(2).

The quotient is x^2-5x+6 when the polynomial p(x) is divided by (x-1), and the remainder is 7.Then:- p(x)=(.....) (……...)+7.Complete it.

Consider the polynomial P(x)=ax^3-x^2-bx-1 Will, P(x) have both (x+1) and (x-1) as factors for any numbers a and b? Justify.

For a ne b, if the equation x ^(2) + ax + b =0 and x ^(2) + bx + a =0 have a common root, then the value of a + b equals to: